In vitro Biofluid Mechanics - Biofluidmechanics: An Introduction to Fluid Mechanics Macrocirculation and Microcirculation - page 364

developed (a parabolic profile) at the location where the cells will be subjected to shear.
The wall shear stress can be approximated by the Poiseuille equation and is therefore
only dependent on the inflow flow rate, the fluid viscosity, and the channel dimensions
(thickness and potentially length). The advantage of this type of system is that cells can
experience a particular shear stress (if adhered to the bottom plate) or can be subjected
to varying shear stresses if they are in the fluid solution (similar to the in vivo conditions
for blood cells).
A slight modification of the parallel plate system is termed the radial parallel plate flow
chamber ( Figure 14.3 ). In this case, fluid flows in from an opening within the center of the
plate, and it exits out in all radial directions. The shear stress is dependent on the radial
position and therefore is not constant for all cells that may be adhered to the bottom sur-
face of the plate. The shear stress gradients need to be accounted for in data analysis
techniques, and therefore, the data may not be as easy to report (e.g., one shear stress
value) for cells adhered to the bottom surface in the parallel plate studies. It is typical in a
flow chamber to use steady flow (instead of pulsatile), which also makes it difficult to
quantify the effect of flow in relation to the physiological in vivo conditions. However,
with the addition of pulsatile flow, the data quantification and data representation become
more challenging.
Viscometer-based systems are most commonly used to expose cells in solution (e.g.,
blood cells) to a uniform shear stress, meaning that the shear stress throughout the fluid
has the same value. Cells can be grown on the bottom surface, but there is no advantage
of this type of system as compared to the parallel plate system for adherent cells. In these
systems, the velocity profile is linear (not parabolic) because one of the constraining walls
is moving, while the other is held fixed. In cone-and-plate viscometry, a cone (the top
plate) is rotated to generate the flow profile ( Figure 14.4 ). The cone has to have a small
incident angle so that the velocity profile does not become disrupted (e.g., is no longer lin-
ear or turbulent) when the distance between the cone and the plate increases. In these sys-
tems, the fluid velocity is dependent on the angular velocity of the cone, the cone angle,
and the distance between the plate and the cone. The shear stress in these systems is only
dependent on the viscosity, the angular velocity, and the cone angle, which are all typi-
cally held constant in experiments. The cone's angular velocity can be modulated to mimic
transient waveforms. This is an advantage over parallel plate experiments where it is nor-
mally more difficult to control the fluid flow rate. Again, there could be a slight variation
to this design, where the top disc would be parallel to the bottom plate. This is termed the
parallel disc viscometer. The velocity is then dependent on the radial location, and the
shear stress is no longer constant throughout the flow field. This arrangement is less com-
mon than the previous three methods discussed.

FIGURE 14.4 Schematic of a cone-and-plate viscometer. In these sys-

tems, cells within the fluid would be subjected to a uniform shear stress,
which is only dependent on the fluid viscosity and the angular rotation
of the cone. This is the case if the angle between the cone and the plate
remains small, so that the velocity profile is linear.

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